The full reasoning can be found below the Sudoku.
May 03 - Super Hard
Puzzle Copyright © Kevin Stone
Share link:
Reasoning
R3C5 is the only square in row 3 that can be <4>
R3C7 is the only square in row 3 that can be <7>
R6C6 is the only square in row 6 that can be <7>
Squares R5C1 and R5C3 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C4 - removing <46> from <2468> leaving <28>
R5C5 - removing <6> from <23568> leaving <2358>
R5C9 - removing <4> from <134> leaving <13>
Squares R5C1 and R5C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C2 - removing <6> from <369> leaving <39>
Squares R4C2 and R6C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C2 - removing <9> from <1689> leaving <168>
R3C2 - removing <9> from <569> leaving <56>
R7C2 - removing <9> from <1689> leaving <168>
R9C2 - removing <9> from <589> leaving <58>
R3C3 is the only square in row 3 that can be <9>
Intersection of column 9 with block 9. The value <4> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C8 - removing <4> from <248> leaving <28>
Intersection of block 6 with row 5. The value <3> only appears in one or more of squares R5C7, R5C8 and R5C9 of block 6. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
R5C5 - removing <3> from <2358> leaving <258>
Intersection of block 8 with column 5. The value <2> only appears in one or more of squares R7C5, R8C5 and R9C5 of block 8. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain this value.
R1C5 - removing <2> from <269> leaving <69>
R5C5 - removing <2> from <258> leaving <58>
R1C1 is the only square in row 1 that can be <2>
Squares R3C2 and R3C8 in row 3, R6C5 and R6C8 in row 6 and R9C2 and R9C5 in row 9 form a Swordfish pattern on possibility <5>. All other instances of this possibility in columns 2, 5 and 8 can be removed.
R5C5 - removing <5> from <58> leaving <8>
R5C4 can only be <2>
R2C6 is the only square in row 2 that can be <2>
R8C4 is the only square in column 4 that can be <8>
Squares R5C1, R5C3, R8C1 and R8C3 form a Type-3 Unique Rectangle on <46>. Upon close inspection, it is clear that:
(R8C1 or R8C3)<59> and R8C6<59> form a naked pair on <59> in row 8. No other squares in the row can contain these possibilities
R8C7 - removing <9> from <369> leaving <36>
R8C9 - removing <9> from <349> leaving <34>
Squares R4C2, R6C2, R4C5 and R6C5 form a Type-4 Unique Rectangle on <39>.
R4C5 - removing <9> from <369> leaving <36>
R6C5 - removing <9> from <359> leaving <35>
Squares R3C2 (XY), R9C2 (XZ) and R2C1 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R9C1 - removing <8> from <489> leaving <49>
R1C2 - removing <8> from <168> leaving <16>
R2C1 is the only square in column 1 that can be <8>
Squares R4C6 (XY), R4C8 (XZ) and R6C4 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R6C8 - removing <4> from <45> leaving <5>
R4C4 - removing <4> from <469> leaving <69>
R6C5 can only be <3>
R3C8 can only be <6>
R5C7 can only be <3>
R3C2 can only be <5>
R5C9 can only be <1>
R8C7 can only be <6>
R5C6 can only be <5>
R2C9 can only be <9>
R4C8 can only be <4>
R6C2 can only be <9>
R4C5 can only be <6>
R7C7 can only be <9>
R2C4 can only be <6>
R2C7 can only be <5>
R1C9 can only be <8>
R9C2 can only be <8>
R4C4 can only be <9>
R1C5 can only be <9>
R8C6 can only be <9>
R6C4 can only be <4>
R4C2 can only be <3>
R7C5 can only be <2>
R8C1 can only be <4>
R4C6 can only be <1>
R9C8 can only be <2>
R9C9 can only be <4>
R9C5 can only be <5>
R7C8 can only be <8>
R9C1 can only be <9>
R8C9 can only be <3>
R1C8 can only be <1>
R2C3 can only be <1>
R8C3 can only be <5>
R5C1 can only be <6>
R1C2 can only be <6>
R7C3 can only be <6>
R5C3 can only be <4>
R7C2 can only be <1>
Today's Sudoku Puzzles
All daily items change at midnight GMT – set your local time zone.
Note: BrainBashers has a Dark Mode option – I recommend not using your browser's dark mode or extensions for BrainBashers